1. Field of the Invention
This invention relates to elimination or improvements of second order and higher (even) order distortion products in differential push-pull amplifiers and circuits, and more specifically to exemplary push-pull amplifiers used in multichannel systems such as cable TV (CATV) head-ends distribution, amplifiers in CATV plants or in subscribers homes, necessary for transmission of analog TV signals, digital QAM signals used in digital TV and high speed modems for Internet communications, and more particularly to use of this method in improved agile frequency conversion apparatus (up-converter), to ensure that distortion specification for the multichannel system is met, but also in high speed digital, GHz range differential clock drives requiring very good balance and duty cycle, and other applications requiring good signal balance and low distortions.
2. Background of the Related Art
In cable television multichannel systems, the frequency band allocated for the service spans over several octaves, from about 50 MHz through 870 Hz and above. In this, and other multi-octave systems many distortion products, such as second harmonic, third harmonic and in some cases higher order harmonics, if any, fall in-band, i.e. fall on other simultaneously transmitted channels in the band, where such harmonic distortion products can cause signal quality degradation and overall system performance degradation. Particularly troublesome is the second harmonic product, which is often the strongest and most notorious term. Attenuating these distortion components to reach acceptable levels of system performance poses one of the more significant and challenging problems faced by designers of such broadband multichannel systems.
By far the most widely used solution in the prior art addressing second harmonic distortion problem is the infamous push-pull amplifier, illustrated in FIG. 1A. The push-pull topology and it's merits are well known and documented in the industry. The main value of a push-pull structure is in it's inherent ability to cancel the second order and other even order distortion terms.
The basic principle of the second harmonic cancellation can be understood by inspecting FIG. 1A. A spectrally clean, harmonic-free input signal of frequency fs, as illustrated in spectrum plot 4, is split by transformer 6 in two arms: the in phase arm 8 and out-of phase arm 10. The complementary phase relationship of the two signals is depicted by the sense of the arrows in spectrum plots 12 and 14. These signals are amplified in inverting amplifiers 16 and 18. Each amplifier is an inverter, having a gain (−A) and non-linear second order distortion, designated as D. The non-linearity of each amplifier generates second harmonic distortion (at frequency 2 fs) which appears at each of the outputs 24 and 26), along with the fundamental frequency fs, as shown in spectrum plots 28 and 30, where the relative level of fundamental signals fs is designated as 0 dB and the level of second harmonics as Dn. While fundamental signals fs at the output of the amplifiers remain out-of-phase with one another, the second harmonics are in phase with each other. This is because the second harmonic is generated by the quadratic non-linearity of the amplifier, and therefore is proportional to the square of the fundamental signals as expressed in eq. (1) below. By operation of squaring, the sign difference between the two arms disappears, and it results in both arms having the same (positive) sign of the second order term.
The output transformer 32 performs the operation of subtraction of the two output signals 24 and 26. The subtraction results in summation of fundamental signals (as well as odd order distortion terms), since they are out of phase with one another, and canceling of the second harmonics, since they are in phase with each other. The cancellation will occur in the same way with all other even order harmonics, (fourth, sixth, etc.). However, the higher order terms are progressively much lower than the second harmonic and are usually negligible. The summation of fundamental signals results in 6 dB level (voltage) increase, and the distortion level is reduced to a residual level of εDn, as depicted in the output spectrum plot 34.
It is well known in the art that the improvement in the distortion with push-pull structure directly depends on the circuit balance, such as the balance of amplifiers gain and impedance match, symmetry and matching of the baluns (BALanced to UNbalanced transformers), etc. Any imbalance in the circuit will reduce the amount of achievable cancellation of second and higher order distortion terms. With reference to FIG. 1A, the signal at the output 36 of the push-pull amplifier can be represented with the following equation:
                    Vout        =                              G            n                    ·                      [                          Vin              +                              ɛ                ·                                                                            D                      n                                        ⁡                                          (                                              Vin                        2                                            )                                                        2                                                      ]                                              (        1        )            where:                Vout=output signal voltage        Vin=input signal voltage        Gn=gain of each arm        Dn=second order distortion in each arm (ratio of distortion voltage and signal voltage)        ε=total imbalance in the push-pull circuit        
From eq. (1) it can be found that the second harmonic improvement due to push-pull topology over single ended amplifier is equal to 20 log (ε). For a theoretical case of ε=0 (perfect balance), the distortion term would be completely canceled. In practice, in a well designed CATV push-pull circuit, using state of the art RF integrated circuits (RFIC) with dual monolithic matched amplifiers and well built baluns, the achievable improvement of the second harmonic distortion is limited by circuit imbalances to no better than 20 to 25 dB (ε in the order of 0.1) over that of a single-ended amplifier.
For additional distortion improvements, the most extensively used method in the prior art is the negative feedback applied to each of the two push-pull amplifiers. It is well known in the art that negative feedback improves linearity and reduces distortion, not only of second order terms, but also of all other even and odd order distortion terms. However, the down side of the negative feedback is that it causes reduction of the amplifier gain, as shown in eq. (4) below. In consequence, to maintain the same RF output power, this loss of gain must be compensated by increase of the input drive level to the push-pull stage. This places additional burden on the previous (driver) stage, requiring both higher gain and higher output level signal handling capability of that stage. The acceptable reduction in gain is often the limit of how strong a negative feedback can be applied. The trade-off between distortion improvements and loss of gain with negative feedback can be found with the help of equations (2) through (7).
The gain of a single-ended amplifier without a feedback can be expressed with equation (2) and the distortion of the same amplifier with eq. (3):
                              Signal          ⁢                                          ⁢          Gain          ⁢                                          ⁢                      (                          without              ⁢                                                          ⁢              FB                        )                          =                              Vos            Vis                    =                      -            A                                              (        2        )                                          Output          ⁢                                          ⁢          Distortion          ⁢                                          ⁢                      (                          without              ⁢                                                          ⁢              FB                        )                          =                  D          =                      Vd            Vos                                              (        3        )            where:                Vis=input signal voltage        Vos=output signal voltage        Vd=distortion signal voltage at amplifier output        
Adding negative feedback to the amplifier, the gain and distortion of the feedback amplifier can be derived with the help of FIG. 1B and FIG. 1C, respectively.
                              Signal          ⁢                                          ⁢          Gain          ⁢                                          ⁢                      (                          with              ⁢                                                          ⁢              negative              ⁢                                                          ⁢              FB                        )                          =                              G            n                    =                                    Vos              Vis                        =                                          -                A                                            1                +                                                      β                    n                                    ⁢                  A                                                                                        (        4        )                                                                                    Output                ⁢                                                                  ⁢                Distortion                ⁢                                                                  ⁢                Level                ⁢                                                                  ⁢                                  (                                      with                    ⁢                                                                                  ⁢                    negative                    ⁢                                                                                  ⁢                    FB                                    )                                            =              Vod                                                                          =                              Vd                                  1                  +                                                            β                      n                                        ⁢                    A                                                                                                          (        5        )            where Vod is output distortion voltage, βn is the negative feedback ratio coefficient and (−A) is the amplifier gain.
The non-linear distortion in most amplifiers occurs at the amplifier's output, because that's where the signal levels are the highest and a load is driven. This assumption is used in the model for distortion in FIG. 1C, where the distortion voltage Vd is shown as if being injected at the output of the amplifier. Eq. (5) was derived based on this model.
In the above equations, both quantities βn and A can be complex numbers. The phase margin of the open loop gain, (βnA) must be sufficient in order to maintain stability and prevent positive feedback and potential parasitic oscillations. Ideal phase of the open loop gain βnA is 0°. The rule of thumb for the phase margin in general is that it should not exceed 60° in order to maintain circuit stability.
Dividing eq. (5) by Vos and substituting eq. (3) in (5), distortion improvement due to negative feedback can be computed:
                              Output          ⁢                                          ⁢          Distortion          ⁢                                          ⁢                      (                          with              ⁢                                                          ⁢              negative              ⁢                                                          ⁢              FB                        )                          =                              D            n                    =                                    Vod              Vos                        =                          D                              (                                  1                  +                                                            β                      n                                        ⁢                    A                                                  )                                                                        (        6        )            
From eq. (4) it can be seen that the gain reduction due to negative feedback is equal to the magnitude |1+βnA| of the denominator, and from eq. (6) it follows that the distortion is improved exactly by the same factor.
Substituting eq. (4) and (6) in eq. (1), the equation for the output signal of the push-pull amplifier of FIG. 1A, a consolidated equation expressing the effects of the negative feedback can be obtained:
                              Vout          ⁢                                          ⁢                      (                          with              ⁢                                                          ⁢              negative              ⁢                                                          ⁢              FB                        )                          =                              A                          (                              1                +                                                      β                    n                                    ⁢                  A                                            )                                ⁡                      [                          Vin              +                              ɛ                ⁢                                  D                                      (                                          1                      +                                                                        β                          n                                                ⁢                        A                                                              )                                                  ⁢                                                      (                                          Vin                      2                                        )                                    2                                                      ]                                              (        7        )            
With eq. (7), the same conclusion reached previously can be confirmed, and that is that with negative feedback the distortion is improved at the expense of gain, and consequently the improvement is limited by the available excess gain of the amplifier, as well as by the available gain and signal handling capabilities of the previous stages driving the push-pull amplifier necessary to compensate for the loss of gain.
Distortion improvement achievable in practical RF amplifiers with negative feedback is typically 3 to 6 dB. As an example, if the amplifier gain is A=14 dB feedback ratio βn=−20 dB, the open loop gain βnA will be equal to −6 dB. Assuming 0° phase shift in the feedback network, the magnitude, |1+βnA| will be equal to 1.5 (or 3.5 dB). In this example, the improvement of the distortion is 3.5 dB, but at the expense of reduction of gain by the same amount of 3.5 dB (gain will drop from 14 dB to 10.5 dB). Increasing feedback coefficient βn much beyond the value in this example would quickly become prohibitive due to excessive loss of gain.
For performance improvements beyond those achievable with negative feedback in push-pull amplifiers, prior art resorts to one or more of the following methods.
Increasing linearity of amplifiers by using higher power amplifiers having higher bias (current and/or voltage) or paralleling multiple amplifiers (such as in power-doublers, where two amplifiers are wired—or to achieve better linearity). The penalty with this approach is in the increased power consumption, size and cost.
Another method to increase linearity often employed in prior art is by using linearization techniques, based either on predistortion or feed-forward methods. The predistortion method utilizes a non-linear module inserted at the input of the amplifier. This module is designed to generate distortion products precisely in anti-phase with the distortion products of the amplifier, thus canceling or reducing the distortion at the output. Another common approach, the feed-forward method, relies on extracting the distortion terms by subtracting the scaled version of the output with the input signal, inverting these distortion terms and injecting them, at the correct level and phase, at the output and thus canceling or reducing the distortion at the output. Both of these methods suffer of increased complexity and difficulties in maintaining the proper phase and amplitude matching conditions due to unit to unit component variation and over wide frequency range, as well as over varying operating conditions (temperature, power supply). In many applications, increased complexity, size and cost of these solutions are prohibitive.
Another way in prior art of improving or removing harmonic products is by way of filtering. Unfortunately this approach can't be used in many CATV devices, namely in those that must have simultaneous bandwidth covering the whole operating frequency range (e.g. distribution amplifiers passing all channels simultaneously). While filtering could be used in frequency agile applications which process one channel at the time and therefore do not need wide simultaneous bandwidth (such as up-converters, channel processors etc.), it would nonetheless complicate the design and increase the size and cost of these devices.
In today's CATV systems, it is expected that each channel should have no less than 65 dB attenuation of distortion (and any other undesired) components. This is often difficult to achieve with the prior art solutions, particularly in applications where power consumption, physical size and cost are important or critical considerations.
Examples of prior art systems embodying one of more of the above features are disclosed in U.S. Pat. No. 3,699,465 to Pranke; U.S. Pat. No. 5,568,089 to Maru; U.S. Pat. No. 6,211,734 to Ahn; U.S. Pat. No. 5,281,924 to Maloberti et al. U.S. Pat. No. 3,895,306 to Rebeles; U.S. Pat. No. 4,933,644 to Fattaruso et al.; U.S. Pat. No. 5,381,112 to Rybicki et al.; and U.S. Pat. No. 5,475,323 to Harris et al. The contents of each of these U.S. patents is incorporated herein by reference in its entirety.
Thus, there is room in the art for improved push-pull amplifiers, suitable for use in agile up-converters and other CATV signal processing components in broadband multicarrier systems and in other applications, ones that sufficiently suppress undesirable distortion components in the composite signal in order to meet and preferably exceed the distortion specification for the system, but inexpensive and easy to design and implement, and suitable for integration in radio frequency integrated circuits (RFICs), without the need for large numbers of costly switched filters and/or power hungry amplifiers.